An Introduction to Computational Learning Theory - download pdf or read online

By Michael J. Kearns

ISBN-10: 0262111934

ISBN-13: 9780262111935

Emphasizing problems with computational potency, Michael Kearns and Umesh Vazirani introduce a few vital subject matters in computational studying concept for researchers and scholars in synthetic intelligence, neural networks, theoretical computing device technological know-how, and statistics.Computational studying conception is a brand new and swiftly increasing region of study that examines formal types of induction with the ambitions of researching the typical tools underlying effective studying algorithms and deciding on the computational impediments to learning.Each subject within the booklet has been selected to explain a basic precept, that's explored in an exact formal surroundings. instinct has been emphasised within the presentation to make the fabric available to the nontheoretician whereas nonetheless delivering unique arguments for the professional. This stability is the results of new proofs of validated theorems, and new displays of the traditional proofs.The issues coated contain the inducement, definitions, and basic effects, either confident and destructive, for the commonly studied L. G. Valiant version of doubtless nearly right studying; Occam's Razor, which formalizes a dating among studying and information compression; the Vapnik-Chervonenkis measurement; the equivalence of vulnerable and robust studying; effective studying within the presence of noise by means of the strategy of statistical queries; relationships among studying and cryptography, and the ensuing computational boundaries on effective studying; reducibility among studying difficulties; and algorithms for studying finite automata from lively experimentation.

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Extra resources for An Introduction to Computational Learning Theory

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Is at least as expressive as C and so there is a representation in 'H. of every function in C . We will refer to 'If as the hypothesis class of the PA C J I learning algorithm. pter 1 26 necessary restrictions on 11, neither do we want to leave 11 entirely uncon­ strained. In particular, it would be senseless to study a model of learning in which the learning algorithm is constrained to run in polynomial time, but the hypotheses output by this learning algorithm could not even be evaluated in polynomial time.

Ml � mlog(l/{l e» -log(l/«5). U sing the fact that log (l / ( l - e)) = a(e), we get the statement of the theorem. 2) and the target dis tribution 1>. 8)-Occam algorithm L might output when given as input a labeled sample S of cardinality m. tn,m/ + 1 I be log 6 Copyrighted Material - «5 provided Occam's Razor 37 The above condition can be satisfied by picking m s uch that both m � (2/bf) log l'Hn,ml and m � (2/bf) 10g ( 1 /o } hold. 1) the statement of the theorem. 3. 3, we interpreted en as an let Xn = {o,l}n.

Blum [78], and Exercise (see also the paper Ehrenfeucht and Haussler [32]). Relationships between various measures of hypothesis complexity and generalization ability have been proposed and examined in a a large and fascinating literature that predates the PAC model results given here. Two dominant theories along these lines are the structural risk mini­ mization of Vapnik of Rissanen [77}. [94] and the minimum description length principle The papers of Quinlan and Rivest [75} and DeSantis, Markowsky and Wegman [29] examine variants of the minimum descrip­ tion length principle from a computational learning theory viewpoint.

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An Introduction to Computational Learning Theory by Michael J. Kearns


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